Properties

Label 1849.4.a.j.1.39
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(50\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.39
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.52844 q^{2} +3.06369 q^{3} +4.44988 q^{4} +14.8551 q^{5} +10.8100 q^{6} +18.1642 q^{7} -12.5264 q^{8} -17.6138 q^{9} +O(q^{10})\) \(q+3.52844 q^{2} +3.06369 q^{3} +4.44988 q^{4} +14.8551 q^{5} +10.8100 q^{6} +18.1642 q^{7} -12.5264 q^{8} -17.6138 q^{9} +52.4155 q^{10} -54.4158 q^{11} +13.6330 q^{12} -71.7442 q^{13} +64.0913 q^{14} +45.5115 q^{15} -79.7976 q^{16} -70.3013 q^{17} -62.1493 q^{18} +71.5106 q^{19} +66.1036 q^{20} +55.6494 q^{21} -192.003 q^{22} +107.841 q^{23} -38.3769 q^{24} +95.6754 q^{25} -253.145 q^{26} -136.683 q^{27} +80.8285 q^{28} -165.324 q^{29} +160.585 q^{30} -117.051 q^{31} -181.350 q^{32} -166.713 q^{33} -248.054 q^{34} +269.832 q^{35} -78.3794 q^{36} +37.0649 q^{37} +252.321 q^{38} -219.802 q^{39} -186.081 q^{40} +24.0387 q^{41} +196.356 q^{42} -242.144 q^{44} -261.656 q^{45} +380.509 q^{46} -454.480 q^{47} -244.475 q^{48} -13.0614 q^{49} +337.585 q^{50} -215.381 q^{51} -319.253 q^{52} -662.454 q^{53} -482.277 q^{54} -808.355 q^{55} -227.532 q^{56} +219.086 q^{57} -583.337 q^{58} +325.977 q^{59} +202.521 q^{60} +545.470 q^{61} -413.009 q^{62} -319.941 q^{63} -1.50096 q^{64} -1065.77 q^{65} -588.236 q^{66} +976.139 q^{67} -312.832 q^{68} +330.390 q^{69} +952.086 q^{70} +494.649 q^{71} +220.638 q^{72} -462.528 q^{73} +130.781 q^{74} +293.119 q^{75} +318.213 q^{76} -988.420 q^{77} -775.557 q^{78} +51.1561 q^{79} -1185.41 q^{80} +56.8202 q^{81} +84.8190 q^{82} +391.041 q^{83} +247.633 q^{84} -1044.34 q^{85} -506.502 q^{87} +681.633 q^{88} -1096.04 q^{89} -923.237 q^{90} -1303.18 q^{91} +479.877 q^{92} -358.609 q^{93} -1603.60 q^{94} +1062.30 q^{95} -555.599 q^{96} -685.682 q^{97} -46.0864 q^{98} +958.470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.52844 1.24749 0.623746 0.781627i \(-0.285610\pi\)
0.623746 + 0.781627i \(0.285610\pi\)
\(3\) 3.06369 0.589607 0.294803 0.955558i \(-0.404746\pi\)
0.294803 + 0.955558i \(0.404746\pi\)
\(4\) 4.44988 0.556235
\(5\) 14.8551 1.32868 0.664342 0.747428i \(-0.268712\pi\)
0.664342 + 0.747428i \(0.268712\pi\)
\(6\) 10.8100 0.735529
\(7\) 18.1642 0.980775 0.490388 0.871504i \(-0.336855\pi\)
0.490388 + 0.871504i \(0.336855\pi\)
\(8\) −12.5264 −0.553593
\(9\) −17.6138 −0.652364
\(10\) 52.4155 1.65752
\(11\) −54.4158 −1.49154 −0.745772 0.666201i \(-0.767919\pi\)
−0.745772 + 0.666201i \(0.767919\pi\)
\(12\) 13.6330 0.327960
\(13\) −71.7442 −1.53064 −0.765318 0.643652i \(-0.777418\pi\)
−0.765318 + 0.643652i \(0.777418\pi\)
\(14\) 64.0913 1.22351
\(15\) 45.5115 0.783401
\(16\) −79.7976 −1.24684
\(17\) −70.3013 −1.00297 −0.501487 0.865165i \(-0.667214\pi\)
−0.501487 + 0.865165i \(0.667214\pi\)
\(18\) −62.1493 −0.813818
\(19\) 71.5106 0.863456 0.431728 0.902004i \(-0.357904\pi\)
0.431728 + 0.902004i \(0.357904\pi\)
\(20\) 66.1036 0.739061
\(21\) 55.6494 0.578272
\(22\) −192.003 −1.86069
\(23\) 107.841 0.977666 0.488833 0.872377i \(-0.337423\pi\)
0.488833 + 0.872377i \(0.337423\pi\)
\(24\) −38.3769 −0.326402
\(25\) 95.6754 0.765403
\(26\) −253.145 −1.90946
\(27\) −136.683 −0.974245
\(28\) 80.8285 0.545541
\(29\) −165.324 −1.05862 −0.529310 0.848429i \(-0.677549\pi\)
−0.529310 + 0.848429i \(0.677549\pi\)
\(30\) 160.585 0.977286
\(31\) −117.051 −0.678163 −0.339082 0.940757i \(-0.610116\pi\)
−0.339082 + 0.940757i \(0.610116\pi\)
\(32\) −181.350 −1.00183
\(33\) −166.713 −0.879424
\(34\) −248.054 −1.25120
\(35\) 269.832 1.30314
\(36\) −78.3794 −0.362868
\(37\) 37.0649 0.164687 0.0823437 0.996604i \(-0.473759\pi\)
0.0823437 + 0.996604i \(0.473759\pi\)
\(38\) 252.321 1.07715
\(39\) −219.802 −0.902473
\(40\) −186.081 −0.735551
\(41\) 24.0387 0.0915662 0.0457831 0.998951i \(-0.485422\pi\)
0.0457831 + 0.998951i \(0.485422\pi\)
\(42\) 196.356 0.721389
\(43\) 0 0
\(44\) −242.144 −0.829648
\(45\) −261.656 −0.866786
\(46\) 380.509 1.21963
\(47\) −454.480 −1.41048 −0.705241 0.708968i \(-0.749161\pi\)
−0.705241 + 0.708968i \(0.749161\pi\)
\(48\) −244.475 −0.735144
\(49\) −13.0614 −0.0380799
\(50\) 337.585 0.954834
\(51\) −215.381 −0.591361
\(52\) −319.253 −0.851393
\(53\) −662.454 −1.71689 −0.858444 0.512907i \(-0.828569\pi\)
−0.858444 + 0.512907i \(0.828569\pi\)
\(54\) −482.277 −1.21536
\(55\) −808.355 −1.98179
\(56\) −227.532 −0.542951
\(57\) 219.086 0.509099
\(58\) −583.337 −1.32062
\(59\) 325.977 0.719299 0.359650 0.933087i \(-0.382896\pi\)
0.359650 + 0.933087i \(0.382896\pi\)
\(60\) 202.521 0.435755
\(61\) 545.470 1.14492 0.572461 0.819932i \(-0.305989\pi\)
0.572461 + 0.819932i \(0.305989\pi\)
\(62\) −413.009 −0.846003
\(63\) −319.941 −0.639822
\(64\) −1.50096 −0.00293156
\(65\) −1065.77 −2.03373
\(66\) −588.236 −1.09707
\(67\) 976.139 1.77992 0.889958 0.456042i \(-0.150733\pi\)
0.889958 + 0.456042i \(0.150733\pi\)
\(68\) −312.832 −0.557889
\(69\) 330.390 0.576438
\(70\) 952.086 1.62566
\(71\) 494.649 0.826818 0.413409 0.910546i \(-0.364338\pi\)
0.413409 + 0.910546i \(0.364338\pi\)
\(72\) 220.638 0.361144
\(73\) −462.528 −0.741573 −0.370787 0.928718i \(-0.620912\pi\)
−0.370787 + 0.928718i \(0.620912\pi\)
\(74\) 130.781 0.205446
\(75\) 293.119 0.451287
\(76\) 318.213 0.480284
\(77\) −988.420 −1.46287
\(78\) −775.557 −1.12583
\(79\) 51.1561 0.0728546 0.0364273 0.999336i \(-0.488402\pi\)
0.0364273 + 0.999336i \(0.488402\pi\)
\(80\) −1185.41 −1.65665
\(81\) 56.8202 0.0779427
\(82\) 84.8190 0.114228
\(83\) 391.041 0.517137 0.258568 0.965993i \(-0.416749\pi\)
0.258568 + 0.965993i \(0.416749\pi\)
\(84\) 247.633 0.321655
\(85\) −1044.34 −1.33264
\(86\) 0 0
\(87\) −506.502 −0.624169
\(88\) 681.633 0.825709
\(89\) −1096.04 −1.30540 −0.652698 0.757618i \(-0.726363\pi\)
−0.652698 + 0.757618i \(0.726363\pi\)
\(90\) −923.237 −1.08131
\(91\) −1303.18 −1.50121
\(92\) 479.877 0.543812
\(93\) −358.609 −0.399850
\(94\) −1603.60 −1.75956
\(95\) 1062.30 1.14726
\(96\) −555.599 −0.590683
\(97\) −685.682 −0.717737 −0.358869 0.933388i \(-0.616837\pi\)
−0.358869 + 0.933388i \(0.616837\pi\)
\(98\) −46.0864 −0.0475044
\(99\) 958.470 0.973029
\(100\) 425.744 0.425744
\(101\) 991.235 0.976550 0.488275 0.872690i \(-0.337626\pi\)
0.488275 + 0.872690i \(0.337626\pi\)
\(102\) −759.959 −0.737717
\(103\) −1673.10 −1.60054 −0.800270 0.599639i \(-0.795311\pi\)
−0.800270 + 0.599639i \(0.795311\pi\)
\(104\) 898.696 0.847350
\(105\) 826.681 0.768341
\(106\) −2337.43 −2.14180
\(107\) 511.415 0.462059 0.231030 0.972947i \(-0.425791\pi\)
0.231030 + 0.972947i \(0.425791\pi\)
\(108\) −608.222 −0.541909
\(109\) −112.112 −0.0985176 −0.0492588 0.998786i \(-0.515686\pi\)
−0.0492588 + 0.998786i \(0.515686\pi\)
\(110\) −2852.23 −2.47227
\(111\) 113.555 0.0971007
\(112\) −1449.46 −1.22287
\(113\) 1391.69 1.15858 0.579290 0.815122i \(-0.303330\pi\)
0.579290 + 0.815122i \(0.303330\pi\)
\(114\) 773.032 0.635097
\(115\) 1601.99 1.29901
\(116\) −735.674 −0.588841
\(117\) 1263.69 0.998532
\(118\) 1150.19 0.897319
\(119\) −1276.97 −0.983693
\(120\) −570.095 −0.433686
\(121\) 1630.08 1.22470
\(122\) 1924.66 1.42828
\(123\) 73.6470 0.0539880
\(124\) −520.865 −0.377218
\(125\) −435.622 −0.311706
\(126\) −1128.89 −0.798173
\(127\) 2009.58 1.40410 0.702052 0.712126i \(-0.252268\pi\)
0.702052 + 0.712126i \(0.252268\pi\)
\(128\) 1445.50 0.998169
\(129\) 0 0
\(130\) −3760.51 −2.53706
\(131\) −990.242 −0.660442 −0.330221 0.943904i \(-0.607123\pi\)
−0.330221 + 0.943904i \(0.607123\pi\)
\(132\) −741.852 −0.489166
\(133\) 1298.93 0.846856
\(134\) 3444.25 2.22043
\(135\) −2030.44 −1.29446
\(136\) 880.621 0.555240
\(137\) 1662.89 1.03701 0.518505 0.855075i \(-0.326489\pi\)
0.518505 + 0.855075i \(0.326489\pi\)
\(138\) 1165.76 0.719102
\(139\) 867.074 0.529095 0.264548 0.964373i \(-0.414777\pi\)
0.264548 + 0.964373i \(0.414777\pi\)
\(140\) 1200.72 0.724852
\(141\) −1392.38 −0.831630
\(142\) 1745.34 1.03145
\(143\) 3904.02 2.28301
\(144\) 1405.54 0.813392
\(145\) −2455.92 −1.40657
\(146\) −1632.00 −0.925107
\(147\) −40.0161 −0.0224522
\(148\) 164.934 0.0916048
\(149\) −1411.40 −0.776014 −0.388007 0.921656i \(-0.626836\pi\)
−0.388007 + 0.921656i \(0.626836\pi\)
\(150\) 1034.25 0.562976
\(151\) −1638.02 −0.882781 −0.441390 0.897315i \(-0.645515\pi\)
−0.441390 + 0.897315i \(0.645515\pi\)
\(152\) −895.769 −0.478003
\(153\) 1238.27 0.654304
\(154\) −3487.58 −1.82492
\(155\) −1738.82 −0.901065
\(156\) −978.091 −0.501987
\(157\) −1244.53 −0.632639 −0.316319 0.948653i \(-0.602447\pi\)
−0.316319 + 0.948653i \(0.602447\pi\)
\(158\) 180.501 0.0908855
\(159\) −2029.55 −1.01229
\(160\) −2693.98 −1.33111
\(161\) 1958.84 0.958870
\(162\) 200.487 0.0972328
\(163\) 1756.05 0.843831 0.421915 0.906635i \(-0.361358\pi\)
0.421915 + 0.906635i \(0.361358\pi\)
\(164\) 106.969 0.0509323
\(165\) −2476.55 −1.16848
\(166\) 1379.77 0.645124
\(167\) 179.987 0.0834001 0.0417001 0.999130i \(-0.486723\pi\)
0.0417001 + 0.999130i \(0.486723\pi\)
\(168\) −697.086 −0.320127
\(169\) 2950.23 1.34285
\(170\) −3684.88 −1.66245
\(171\) −1259.58 −0.563287
\(172\) 0 0
\(173\) −3964.61 −1.74233 −0.871167 0.490987i \(-0.836636\pi\)
−0.871167 + 0.490987i \(0.836636\pi\)
\(174\) −1787.16 −0.778646
\(175\) 1737.87 0.750688
\(176\) 4342.25 1.85971
\(177\) 998.693 0.424104
\(178\) −3867.32 −1.62847
\(179\) 3188.70 1.33148 0.665739 0.746185i \(-0.268116\pi\)
0.665739 + 0.746185i \(0.268116\pi\)
\(180\) −1164.34 −0.482137
\(181\) −53.3936 −0.0219266 −0.0109633 0.999940i \(-0.503490\pi\)
−0.0109633 + 0.999940i \(0.503490\pi\)
\(182\) −4598.18 −1.87275
\(183\) 1671.15 0.675054
\(184\) −1350.85 −0.541229
\(185\) 550.604 0.218818
\(186\) −1265.33 −0.498809
\(187\) 3825.50 1.49598
\(188\) −2022.38 −0.784559
\(189\) −2482.73 −0.955515
\(190\) 3748.26 1.43120
\(191\) −222.120 −0.0841466 −0.0420733 0.999115i \(-0.513396\pi\)
−0.0420733 + 0.999115i \(0.513396\pi\)
\(192\) −4.59846 −0.00172847
\(193\) 5074.95 1.89276 0.946380 0.323056i \(-0.104710\pi\)
0.946380 + 0.323056i \(0.104710\pi\)
\(194\) −2419.39 −0.895371
\(195\) −3265.19 −1.19910
\(196\) −58.1217 −0.0211814
\(197\) −2931.10 −1.06006 −0.530032 0.847978i \(-0.677820\pi\)
−0.530032 + 0.847978i \(0.677820\pi\)
\(198\) 3381.90 1.21385
\(199\) 2008.74 0.715556 0.357778 0.933807i \(-0.383535\pi\)
0.357778 + 0.933807i \(0.383535\pi\)
\(200\) −1198.47 −0.423722
\(201\) 2990.58 1.04945
\(202\) 3497.51 1.21824
\(203\) −3002.99 −1.03827
\(204\) −958.420 −0.328935
\(205\) 357.098 0.121663
\(206\) −5903.44 −1.99666
\(207\) −1899.49 −0.637794
\(208\) 5725.02 1.90845
\(209\) −3891.31 −1.28788
\(210\) 2916.89 0.958498
\(211\) 823.929 0.268823 0.134411 0.990926i \(-0.457086\pi\)
0.134411 + 0.990926i \(0.457086\pi\)
\(212\) −2947.84 −0.954993
\(213\) 1515.45 0.487497
\(214\) 1804.50 0.576415
\(215\) 0 0
\(216\) 1712.14 0.539335
\(217\) −2126.15 −0.665126
\(218\) −395.582 −0.122900
\(219\) −1417.04 −0.437237
\(220\) −3597.08 −1.10234
\(221\) 5043.71 1.53519
\(222\) 400.673 0.121132
\(223\) −2138.39 −0.642139 −0.321070 0.947056i \(-0.604042\pi\)
−0.321070 + 0.947056i \(0.604042\pi\)
\(224\) −3294.08 −0.982566
\(225\) −1685.21 −0.499321
\(226\) 4910.51 1.44532
\(227\) 448.136 0.131030 0.0655151 0.997852i \(-0.479131\pi\)
0.0655151 + 0.997852i \(0.479131\pi\)
\(228\) 974.906 0.283179
\(229\) −5716.16 −1.64950 −0.824748 0.565501i \(-0.808683\pi\)
−0.824748 + 0.565501i \(0.808683\pi\)
\(230\) 5652.51 1.62050
\(231\) −3028.21 −0.862517
\(232\) 2070.92 0.586045
\(233\) −6035.33 −1.69694 −0.848471 0.529242i \(-0.822476\pi\)
−0.848471 + 0.529242i \(0.822476\pi\)
\(234\) 4458.85 1.24566
\(235\) −6751.36 −1.87409
\(236\) 1450.56 0.400099
\(237\) 156.726 0.0429556
\(238\) −4505.70 −1.22715
\(239\) 2662.70 0.720653 0.360326 0.932826i \(-0.382665\pi\)
0.360326 + 0.932826i \(0.382665\pi\)
\(240\) −3631.71 −0.976774
\(241\) −81.7963 −0.0218629 −0.0109315 0.999940i \(-0.503480\pi\)
−0.0109315 + 0.999940i \(0.503480\pi\)
\(242\) 5751.63 1.52781
\(243\) 3864.51 1.02020
\(244\) 2427.27 0.636845
\(245\) −194.029 −0.0505962
\(246\) 259.859 0.0673496
\(247\) −5130.47 −1.32164
\(248\) 1466.23 0.375427
\(249\) 1198.03 0.304907
\(250\) −1537.06 −0.388850
\(251\) −3638.89 −0.915078 −0.457539 0.889190i \(-0.651269\pi\)
−0.457539 + 0.889190i \(0.651269\pi\)
\(252\) −1423.70 −0.355891
\(253\) −5868.23 −1.45823
\(254\) 7090.67 1.75161
\(255\) −3199.52 −0.785732
\(256\) 5112.38 1.24814
\(257\) 2962.31 0.719003 0.359502 0.933144i \(-0.382947\pi\)
0.359502 + 0.933144i \(0.382947\pi\)
\(258\) 0 0
\(259\) 673.255 0.161521
\(260\) −4742.55 −1.13123
\(261\) 2912.00 0.690605
\(262\) −3494.01 −0.823895
\(263\) 113.737 0.0266666 0.0133333 0.999911i \(-0.495756\pi\)
0.0133333 + 0.999911i \(0.495756\pi\)
\(264\) 2088.31 0.486843
\(265\) −9840.86 −2.28120
\(266\) 4583.21 1.05645
\(267\) −3357.93 −0.769671
\(268\) 4343.70 0.990051
\(269\) −6938.53 −1.57267 −0.786337 0.617797i \(-0.788025\pi\)
−0.786337 + 0.617797i \(0.788025\pi\)
\(270\) −7164.29 −1.61483
\(271\) 589.833 0.132213 0.0661066 0.997813i \(-0.478942\pi\)
0.0661066 + 0.997813i \(0.478942\pi\)
\(272\) 5609.88 1.25055
\(273\) −3992.53 −0.885123
\(274\) 5867.41 1.29366
\(275\) −5206.25 −1.14163
\(276\) 1470.19 0.320635
\(277\) −5117.30 −1.11000 −0.554998 0.831852i \(-0.687281\pi\)
−0.554998 + 0.831852i \(0.687281\pi\)
\(278\) 3059.42 0.660042
\(279\) 2061.72 0.442409
\(280\) −3380.02 −0.721410
\(281\) −157.427 −0.0334210 −0.0167105 0.999860i \(-0.505319\pi\)
−0.0167105 + 0.999860i \(0.505319\pi\)
\(282\) −4912.94 −1.03745
\(283\) 3584.31 0.752879 0.376440 0.926441i \(-0.377148\pi\)
0.376440 + 0.926441i \(0.377148\pi\)
\(284\) 2201.13 0.459905
\(285\) 3254.55 0.676432
\(286\) 13775.1 2.84804
\(287\) 436.644 0.0898058
\(288\) 3194.27 0.653555
\(289\) 29.2718 0.00595802
\(290\) −8665.56 −1.75469
\(291\) −2100.72 −0.423183
\(292\) −2058.20 −0.412489
\(293\) −6808.92 −1.35761 −0.678807 0.734316i \(-0.737503\pi\)
−0.678807 + 0.734316i \(0.737503\pi\)
\(294\) −141.194 −0.0280089
\(295\) 4842.44 0.955722
\(296\) −464.289 −0.0911698
\(297\) 7437.70 1.45313
\(298\) −4980.03 −0.968071
\(299\) −7736.94 −1.49645
\(300\) 1304.35 0.251021
\(301\) 0 0
\(302\) −5779.64 −1.10126
\(303\) 3036.83 0.575781
\(304\) −5706.37 −1.07659
\(305\) 8103.03 1.52124
\(306\) 4369.18 0.816239
\(307\) 7195.92 1.33776 0.668880 0.743370i \(-0.266774\pi\)
0.668880 + 0.743370i \(0.266774\pi\)
\(308\) −4398.35 −0.813699
\(309\) −5125.86 −0.943689
\(310\) −6135.31 −1.12407
\(311\) −5076.42 −0.925586 −0.462793 0.886466i \(-0.653153\pi\)
−0.462793 + 0.886466i \(0.653153\pi\)
\(312\) 2753.32 0.499603
\(313\) −5157.09 −0.931297 −0.465649 0.884970i \(-0.654179\pi\)
−0.465649 + 0.884970i \(0.654179\pi\)
\(314\) −4391.25 −0.789212
\(315\) −4752.77 −0.850122
\(316\) 227.639 0.0405243
\(317\) −6858.21 −1.21513 −0.607564 0.794271i \(-0.707853\pi\)
−0.607564 + 0.794271i \(0.707853\pi\)
\(318\) −7161.15 −1.26282
\(319\) 8996.26 1.57898
\(320\) −22.2969 −0.00389511
\(321\) 1566.81 0.272433
\(322\) 6911.64 1.19618
\(323\) −5027.29 −0.866024
\(324\) 252.843 0.0433544
\(325\) −6864.15 −1.17155
\(326\) 6196.11 1.05267
\(327\) −343.477 −0.0580866
\(328\) −301.118 −0.0506904
\(329\) −8255.26 −1.38337
\(330\) −8738.34 −1.45767
\(331\) 7748.36 1.28667 0.643336 0.765584i \(-0.277550\pi\)
0.643336 + 0.765584i \(0.277550\pi\)
\(332\) 1740.09 0.287649
\(333\) −652.855 −0.107436
\(334\) 635.074 0.104041
\(335\) 14500.7 2.36495
\(336\) −4440.69 −0.721011
\(337\) −3882.30 −0.627544 −0.313772 0.949498i \(-0.601593\pi\)
−0.313772 + 0.949498i \(0.601593\pi\)
\(338\) 10409.7 1.67519
\(339\) 4263.71 0.683107
\(340\) −4647.17 −0.741259
\(341\) 6369.45 1.01151
\(342\) −4444.33 −0.702696
\(343\) −6467.57 −1.01812
\(344\) 0 0
\(345\) 4907.99 0.765905
\(346\) −13988.9 −2.17355
\(347\) 109.552 0.0169484 0.00847418 0.999964i \(-0.497303\pi\)
0.00847418 + 0.999964i \(0.497303\pi\)
\(348\) −2253.87 −0.347185
\(349\) −6182.65 −0.948280 −0.474140 0.880450i \(-0.657241\pi\)
−0.474140 + 0.880450i \(0.657241\pi\)
\(350\) 6131.96 0.936477
\(351\) 9806.20 1.49121
\(352\) 9868.30 1.49427
\(353\) −8396.83 −1.26606 −0.633029 0.774128i \(-0.718188\pi\)
−0.633029 + 0.774128i \(0.718188\pi\)
\(354\) 3523.83 0.529066
\(355\) 7348.09 1.09858
\(356\) −4877.26 −0.726107
\(357\) −3912.23 −0.579992
\(358\) 11251.1 1.66101
\(359\) −9437.09 −1.38738 −0.693692 0.720272i \(-0.744017\pi\)
−0.693692 + 0.720272i \(0.744017\pi\)
\(360\) 3277.60 0.479847
\(361\) −1745.23 −0.254444
\(362\) −188.396 −0.0273532
\(363\) 4994.05 0.722093
\(364\) −5798.98 −0.835025
\(365\) −6870.93 −0.985317
\(366\) 5896.54 0.842124
\(367\) 9389.93 1.33556 0.667780 0.744359i \(-0.267245\pi\)
0.667780 + 0.744359i \(0.267245\pi\)
\(368\) −8605.42 −1.21899
\(369\) −423.413 −0.0597345
\(370\) 1942.77 0.272973
\(371\) −12033.0 −1.68388
\(372\) −1595.77 −0.222410
\(373\) −443.328 −0.0615406 −0.0307703 0.999526i \(-0.509796\pi\)
−0.0307703 + 0.999526i \(0.509796\pi\)
\(374\) 13498.0 1.86622
\(375\) −1334.61 −0.183784
\(376\) 5692.99 0.780833
\(377\) 11861.1 1.62036
\(378\) −8760.18 −1.19200
\(379\) −4688.25 −0.635407 −0.317704 0.948190i \(-0.602912\pi\)
−0.317704 + 0.948190i \(0.602912\pi\)
\(380\) 4727.11 0.638146
\(381\) 6156.71 0.827869
\(382\) −783.735 −0.104972
\(383\) −3374.31 −0.450180 −0.225090 0.974338i \(-0.572268\pi\)
−0.225090 + 0.974338i \(0.572268\pi\)
\(384\) 4428.57 0.588527
\(385\) −14683.1 −1.94369
\(386\) 17906.6 2.36120
\(387\) 0 0
\(388\) −3051.20 −0.399230
\(389\) −13756.1 −1.79297 −0.896483 0.443078i \(-0.853886\pi\)
−0.896483 + 0.443078i \(0.853886\pi\)
\(390\) −11521.0 −1.49587
\(391\) −7581.33 −0.980574
\(392\) 163.612 0.0210808
\(393\) −3033.79 −0.389401
\(394\) −10342.2 −1.32242
\(395\) 759.932 0.0968008
\(396\) 4265.08 0.541233
\(397\) 6440.24 0.814173 0.407086 0.913390i \(-0.366545\pi\)
0.407086 + 0.913390i \(0.366545\pi\)
\(398\) 7087.70 0.892650
\(399\) 3979.52 0.499312
\(400\) −7634.67 −0.954333
\(401\) 4498.42 0.560200 0.280100 0.959971i \(-0.409632\pi\)
0.280100 + 0.959971i \(0.409632\pi\)
\(402\) 10552.1 1.30918
\(403\) 8397.76 1.03802
\(404\) 4410.88 0.543191
\(405\) 844.073 0.103561
\(406\) −10595.9 −1.29523
\(407\) −2016.92 −0.245638
\(408\) 2697.95 0.327373
\(409\) −749.470 −0.0906086 −0.0453043 0.998973i \(-0.514426\pi\)
−0.0453043 + 0.998973i \(0.514426\pi\)
\(410\) 1260.00 0.151773
\(411\) 5094.58 0.611428
\(412\) −7445.10 −0.890276
\(413\) 5921.12 0.705471
\(414\) −6702.22 −0.795642
\(415\) 5808.98 0.687112
\(416\) 13010.8 1.53343
\(417\) 2656.44 0.311958
\(418\) −13730.2 −1.60662
\(419\) −9940.58 −1.15902 −0.579510 0.814965i \(-0.696756\pi\)
−0.579510 + 0.814965i \(0.696756\pi\)
\(420\) 3678.63 0.427378
\(421\) 3626.40 0.419810 0.209905 0.977722i \(-0.432685\pi\)
0.209905 + 0.977722i \(0.432685\pi\)
\(422\) 2907.18 0.335354
\(423\) 8005.12 0.920148
\(424\) 8298.16 0.950458
\(425\) −6726.10 −0.767680
\(426\) 5347.17 0.608149
\(427\) 9908.03 1.12291
\(428\) 2275.73 0.257013
\(429\) 11960.7 1.34608
\(430\) 0 0
\(431\) 10247.8 1.14529 0.572644 0.819804i \(-0.305918\pi\)
0.572644 + 0.819804i \(0.305918\pi\)
\(432\) 10907.0 1.21473
\(433\) 474.905 0.0527078 0.0263539 0.999653i \(-0.491610\pi\)
0.0263539 + 0.999653i \(0.491610\pi\)
\(434\) −7501.98 −0.829739
\(435\) −7524.16 −0.829324
\(436\) −498.886 −0.0547989
\(437\) 7711.74 0.844171
\(438\) −4999.95 −0.545449
\(439\) −5591.28 −0.607875 −0.303938 0.952692i \(-0.598301\pi\)
−0.303938 + 0.952692i \(0.598301\pi\)
\(440\) 10125.8 1.09711
\(441\) 230.062 0.0248420
\(442\) 17796.4 1.91513
\(443\) 8177.66 0.877048 0.438524 0.898719i \(-0.355501\pi\)
0.438524 + 0.898719i \(0.355501\pi\)
\(444\) 505.307 0.0540108
\(445\) −16281.9 −1.73446
\(446\) −7545.17 −0.801063
\(447\) −4324.08 −0.457543
\(448\) −27.2637 −0.00287520
\(449\) 15836.2 1.66450 0.832248 0.554404i \(-0.187054\pi\)
0.832248 + 0.554404i \(0.187054\pi\)
\(450\) −5946.16 −0.622899
\(451\) −1308.08 −0.136575
\(452\) 6192.87 0.644442
\(453\) −5018.37 −0.520494
\(454\) 1581.22 0.163459
\(455\) −19358.9 −1.99463
\(456\) −2744.36 −0.281834
\(457\) 10990.1 1.12493 0.562465 0.826821i \(-0.309853\pi\)
0.562465 + 0.826821i \(0.309853\pi\)
\(458\) −20169.1 −2.05773
\(459\) 9608.98 0.977143
\(460\) 7128.65 0.722554
\(461\) −6790.50 −0.686041 −0.343021 0.939328i \(-0.611450\pi\)
−0.343021 + 0.939328i \(0.611450\pi\)
\(462\) −10684.8 −1.07598
\(463\) 9388.34 0.942361 0.471180 0.882037i \(-0.343828\pi\)
0.471180 + 0.882037i \(0.343828\pi\)
\(464\) 13192.5 1.31993
\(465\) −5327.19 −0.531274
\(466\) −21295.3 −2.11692
\(467\) −14261.3 −1.41314 −0.706569 0.707644i \(-0.749758\pi\)
−0.706569 + 0.707644i \(0.749758\pi\)
\(468\) 5623.27 0.555418
\(469\) 17730.8 1.74570
\(470\) −23821.8 −2.33791
\(471\) −3812.85 −0.373008
\(472\) −4083.32 −0.398199
\(473\) 0 0
\(474\) 552.999 0.0535867
\(475\) 6841.80 0.660891
\(476\) −5682.35 −0.547164
\(477\) 11668.4 1.12004
\(478\) 9395.19 0.899008
\(479\) −3859.13 −0.368117 −0.184058 0.982915i \(-0.558924\pi\)
−0.184058 + 0.982915i \(0.558924\pi\)
\(480\) −8253.51 −0.784832
\(481\) −2659.19 −0.252076
\(482\) −288.613 −0.0272738
\(483\) 6001.27 0.565356
\(484\) 7253.65 0.681222
\(485\) −10185.9 −0.953646
\(486\) 13635.7 1.27269
\(487\) −7036.51 −0.654732 −0.327366 0.944898i \(-0.606161\pi\)
−0.327366 + 0.944898i \(0.606161\pi\)
\(488\) −6832.77 −0.633821
\(489\) 5379.98 0.497528
\(490\) −684.620 −0.0631184
\(491\) 15125.5 1.39023 0.695116 0.718898i \(-0.255353\pi\)
0.695116 + 0.718898i \(0.255353\pi\)
\(492\) 327.720 0.0300300
\(493\) 11622.5 1.06177
\(494\) −18102.6 −1.64873
\(495\) 14238.2 1.29285
\(496\) 9340.43 0.845559
\(497\) 8984.91 0.810922
\(498\) 4227.17 0.380369
\(499\) 5619.20 0.504108 0.252054 0.967713i \(-0.418894\pi\)
0.252054 + 0.967713i \(0.418894\pi\)
\(500\) −1938.46 −0.173381
\(501\) 551.424 0.0491733
\(502\) −12839.6 −1.14155
\(503\) 1050.56 0.0931258 0.0465629 0.998915i \(-0.485173\pi\)
0.0465629 + 0.998915i \(0.485173\pi\)
\(504\) 4007.71 0.354201
\(505\) 14724.9 1.29753
\(506\) −20705.7 −1.81913
\(507\) 9038.59 0.791751
\(508\) 8942.37 0.781011
\(509\) 2928.22 0.254993 0.127496 0.991839i \(-0.459306\pi\)
0.127496 + 0.991839i \(0.459306\pi\)
\(510\) −11289.3 −0.980193
\(511\) −8401.47 −0.727317
\(512\) 6474.68 0.558873
\(513\) −9774.27 −0.841217
\(514\) 10452.3 0.896951
\(515\) −24854.2 −2.12661
\(516\) 0 0
\(517\) 24730.9 2.10380
\(518\) 2375.54 0.201496
\(519\) −12146.3 −1.02729
\(520\) 13350.3 1.12586
\(521\) 14601.6 1.22785 0.613925 0.789364i \(-0.289590\pi\)
0.613925 + 0.789364i \(0.289590\pi\)
\(522\) 10274.8 0.861524
\(523\) 6271.99 0.524388 0.262194 0.965015i \(-0.415554\pi\)
0.262194 + 0.965015i \(0.415554\pi\)
\(524\) −4406.46 −0.367361
\(525\) 5324.28 0.442611
\(526\) 401.313 0.0332663
\(527\) 8228.87 0.680180
\(528\) 13303.3 1.09650
\(529\) −537.410 −0.0441695
\(530\) −34722.9 −2.84578
\(531\) −5741.71 −0.469245
\(532\) 5780.10 0.471051
\(533\) −1724.64 −0.140154
\(534\) −11848.3 −0.960157
\(535\) 7597.14 0.613931
\(536\) −12227.5 −0.985350
\(537\) 9769.17 0.785048
\(538\) −24482.2 −1.96190
\(539\) 710.748 0.0567979
\(540\) −9035.22 −0.720026
\(541\) 3413.67 0.271285 0.135643 0.990758i \(-0.456690\pi\)
0.135643 + 0.990758i \(0.456690\pi\)
\(542\) 2081.19 0.164935
\(543\) −163.581 −0.0129281
\(544\) 12749.1 1.00481
\(545\) −1665.45 −0.130899
\(546\) −14087.4 −1.10418
\(547\) −258.591 −0.0202131 −0.0101065 0.999949i \(-0.503217\pi\)
−0.0101065 + 0.999949i \(0.503217\pi\)
\(548\) 7399.66 0.576821
\(549\) −9607.81 −0.746906
\(550\) −18369.9 −1.42418
\(551\) −11822.4 −0.914071
\(552\) −4138.59 −0.319112
\(553\) 929.211 0.0714540
\(554\) −18056.1 −1.38471
\(555\) 1686.88 0.129016
\(556\) 3858.37 0.294301
\(557\) 8465.22 0.643955 0.321978 0.946747i \(-0.395652\pi\)
0.321978 + 0.946747i \(0.395652\pi\)
\(558\) 7274.67 0.551902
\(559\) 0 0
\(560\) −21532.0 −1.62481
\(561\) 11720.1 0.882040
\(562\) −555.471 −0.0416924
\(563\) −622.915 −0.0466301 −0.0233150 0.999728i \(-0.507422\pi\)
−0.0233150 + 0.999728i \(0.507422\pi\)
\(564\) −6195.93 −0.462581
\(565\) 20673.8 1.53939
\(566\) 12647.0 0.939210
\(567\) 1032.09 0.0764443
\(568\) −6196.17 −0.457721
\(569\) 6933.34 0.510827 0.255413 0.966832i \(-0.417788\pi\)
0.255413 + 0.966832i \(0.417788\pi\)
\(570\) 11483.5 0.843843
\(571\) −18877.4 −1.38353 −0.691764 0.722123i \(-0.743166\pi\)
−0.691764 + 0.722123i \(0.743166\pi\)
\(572\) 17372.4 1.26989
\(573\) −680.505 −0.0496134
\(574\) 1540.67 0.112032
\(575\) 10317.7 0.748308
\(576\) 26.4376 0.00191244
\(577\) −11798.0 −0.851227 −0.425613 0.904905i \(-0.639942\pi\)
−0.425613 + 0.904905i \(0.639942\pi\)
\(578\) 103.284 0.00743258
\(579\) 15548.0 1.11598
\(580\) −10928.5 −0.782384
\(581\) 7102.96 0.507195
\(582\) −7412.25 −0.527917
\(583\) 36048.0 2.56081
\(584\) 5793.81 0.410530
\(585\) 18772.3 1.32673
\(586\) −24024.8 −1.69361
\(587\) −663.788 −0.0466737 −0.0233368 0.999728i \(-0.507429\pi\)
−0.0233368 + 0.999728i \(0.507429\pi\)
\(588\) −178.067 −0.0124887
\(589\) −8370.42 −0.585564
\(590\) 17086.3 1.19225
\(591\) −8979.98 −0.625021
\(592\) −2957.69 −0.205338
\(593\) 3823.87 0.264802 0.132401 0.991196i \(-0.457731\pi\)
0.132401 + 0.991196i \(0.457731\pi\)
\(594\) 26243.5 1.81277
\(595\) −18969.5 −1.30702
\(596\) −6280.54 −0.431646
\(597\) 6154.14 0.421896
\(598\) −27299.3 −1.86681
\(599\) −4835.69 −0.329851 −0.164926 0.986306i \(-0.552738\pi\)
−0.164926 + 0.986306i \(0.552738\pi\)
\(600\) −3671.73 −0.249829
\(601\) 1776.64 0.120584 0.0602918 0.998181i \(-0.480797\pi\)
0.0602918 + 0.998181i \(0.480797\pi\)
\(602\) 0 0
\(603\) −17193.5 −1.16115
\(604\) −7288.98 −0.491033
\(605\) 24215.1 1.62724
\(606\) 10715.3 0.718281
\(607\) 17302.1 1.15695 0.578477 0.815699i \(-0.303647\pi\)
0.578477 + 0.815699i \(0.303647\pi\)
\(608\) −12968.4 −0.865032
\(609\) −9200.21 −0.612170
\(610\) 28591.1 1.89773
\(611\) 32606.3 2.15893
\(612\) 5510.17 0.363947
\(613\) −18526.0 −1.22065 −0.610323 0.792152i \(-0.708960\pi\)
−0.610323 + 0.792152i \(0.708960\pi\)
\(614\) 25390.3 1.66885
\(615\) 1094.04 0.0717331
\(616\) 12381.3 0.809835
\(617\) 29791.8 1.94387 0.971937 0.235240i \(-0.0755875\pi\)
0.971937 + 0.235240i \(0.0755875\pi\)
\(618\) −18086.3 −1.17724
\(619\) 11505.2 0.747065 0.373533 0.927617i \(-0.378146\pi\)
0.373533 + 0.927617i \(0.378146\pi\)
\(620\) −7737.52 −0.501204
\(621\) −14739.9 −0.952486
\(622\) −17911.8 −1.15466
\(623\) −19908.8 −1.28030
\(624\) 17539.7 1.12524
\(625\) −18430.6 −1.17956
\(626\) −18196.5 −1.16179
\(627\) −11921.7 −0.759344
\(628\) −5538.01 −0.351896
\(629\) −2605.71 −0.165177
\(630\) −16769.9 −1.06052
\(631\) −30684.7 −1.93588 −0.967939 0.251184i \(-0.919180\pi\)
−0.967939 + 0.251184i \(0.919180\pi\)
\(632\) −640.801 −0.0403318
\(633\) 2524.26 0.158500
\(634\) −24198.8 −1.51586
\(635\) 29852.6 1.86561
\(636\) −9031.26 −0.563070
\(637\) 937.081 0.0582865
\(638\) 31742.8 1.96976
\(639\) −8712.67 −0.539386
\(640\) 21473.2 1.32625
\(641\) −12353.5 −0.761209 −0.380605 0.924738i \(-0.624284\pi\)
−0.380605 + 0.924738i \(0.624284\pi\)
\(642\) 5528.41 0.339858
\(643\) 8901.37 0.545934 0.272967 0.962023i \(-0.411995\pi\)
0.272967 + 0.962023i \(0.411995\pi\)
\(644\) 8716.60 0.533357
\(645\) 0 0
\(646\) −17738.5 −1.08036
\(647\) 15209.5 0.924186 0.462093 0.886831i \(-0.347099\pi\)
0.462093 + 0.886831i \(0.347099\pi\)
\(648\) −711.752 −0.0431486
\(649\) −17738.3 −1.07287
\(650\) −24219.7 −1.46150
\(651\) −6513.85 −0.392163
\(652\) 7814.21 0.469368
\(653\) −11591.2 −0.694638 −0.347319 0.937747i \(-0.612908\pi\)
−0.347319 + 0.937747i \(0.612908\pi\)
\(654\) −1211.94 −0.0724626
\(655\) −14710.2 −0.877519
\(656\) −1918.23 −0.114168
\(657\) 8146.90 0.483776
\(658\) −29128.2 −1.72574
\(659\) 15290.8 0.903863 0.451932 0.892053i \(-0.350735\pi\)
0.451932 + 0.892053i \(0.350735\pi\)
\(660\) −11020.3 −0.649948
\(661\) 787.114 0.0463165 0.0231582 0.999732i \(-0.492628\pi\)
0.0231582 + 0.999732i \(0.492628\pi\)
\(662\) 27339.6 1.60511
\(663\) 15452.3 0.905158
\(664\) −4898.33 −0.286283
\(665\) 19295.8 1.12520
\(666\) −2303.56 −0.134026
\(667\) −17828.7 −1.03498
\(668\) 800.921 0.0463901
\(669\) −6551.35 −0.378610
\(670\) 51164.8 2.95025
\(671\) −29682.2 −1.70770
\(672\) −10092.0 −0.579328
\(673\) −10873.2 −0.622783 −0.311391 0.950282i \(-0.600795\pi\)
−0.311391 + 0.950282i \(0.600795\pi\)
\(674\) −13698.4 −0.782855
\(675\) −13077.2 −0.745690
\(676\) 13128.2 0.746938
\(677\) 29398.0 1.66891 0.834457 0.551073i \(-0.185781\pi\)
0.834457 + 0.551073i \(0.185781\pi\)
\(678\) 15044.2 0.852170
\(679\) −12454.9 −0.703939
\(680\) 13081.8 0.737739
\(681\) 1372.95 0.0772563
\(682\) 22474.2 1.26185
\(683\) 23535.9 1.31856 0.659279 0.751899i \(-0.270862\pi\)
0.659279 + 0.751899i \(0.270862\pi\)
\(684\) −5604.96 −0.313320
\(685\) 24702.5 1.37786
\(686\) −22820.4 −1.27010
\(687\) −17512.5 −0.972554
\(688\) 0 0
\(689\) 47527.3 2.62793
\(690\) 17317.5 0.955460
\(691\) 15755.6 0.867397 0.433698 0.901058i \(-0.357208\pi\)
0.433698 + 0.901058i \(0.357208\pi\)
\(692\) −17642.0 −0.969147
\(693\) 17409.9 0.954323
\(694\) 386.549 0.0211429
\(695\) 12880.5 0.703001
\(696\) 6344.64 0.345536
\(697\) −1689.95 −0.0918385
\(698\) −21815.1 −1.18297
\(699\) −18490.4 −1.00053
\(700\) 7733.30 0.417559
\(701\) −11016.5 −0.593564 −0.296782 0.954945i \(-0.595913\pi\)
−0.296782 + 0.954945i \(0.595913\pi\)
\(702\) 34600.6 1.86028
\(703\) 2650.53 0.142200
\(704\) 81.6758 0.00437254
\(705\) −20684.0 −1.10497
\(706\) −29627.7 −1.57940
\(707\) 18005.0 0.957776
\(708\) 4444.06 0.235901
\(709\) 26713.3 1.41500 0.707502 0.706711i \(-0.249822\pi\)
0.707502 + 0.706711i \(0.249822\pi\)
\(710\) 25927.3 1.37047
\(711\) −901.055 −0.0475277
\(712\) 13729.5 0.722659
\(713\) −12622.9 −0.663017
\(714\) −13804.1 −0.723535
\(715\) 57994.8 3.03340
\(716\) 14189.3 0.740614
\(717\) 8157.69 0.424902
\(718\) −33298.2 −1.73075
\(719\) −28318.6 −1.46885 −0.734427 0.678688i \(-0.762549\pi\)
−0.734427 + 0.678688i \(0.762549\pi\)
\(720\) 20879.5 1.08074
\(721\) −30390.6 −1.56977
\(722\) −6157.95 −0.317417
\(723\) −250.598 −0.0128905
\(724\) −237.595 −0.0121963
\(725\) −15817.5 −0.810271
\(726\) 17621.2 0.900805
\(727\) −2736.88 −0.139622 −0.0698111 0.997560i \(-0.522240\pi\)
−0.0698111 + 0.997560i \(0.522240\pi\)
\(728\) 16324.1 0.831060
\(729\) 10305.5 0.523574
\(730\) −24243.6 −1.22917
\(731\) 0 0
\(732\) 7436.41 0.375488
\(733\) −26362.0 −1.32838 −0.664189 0.747565i \(-0.731223\pi\)
−0.664189 + 0.747565i \(0.731223\pi\)
\(734\) 33131.8 1.66610
\(735\) −594.445 −0.0298319
\(736\) −19556.9 −0.979451
\(737\) −53117.4 −2.65482
\(738\) −1493.99 −0.0745182
\(739\) −4576.23 −0.227793 −0.113897 0.993493i \(-0.536333\pi\)
−0.113897 + 0.993493i \(0.536333\pi\)
\(740\) 2450.12 0.121714
\(741\) −15718.2 −0.779245
\(742\) −42457.6 −2.10063
\(743\) −11690.3 −0.577219 −0.288610 0.957447i \(-0.593193\pi\)
−0.288610 + 0.957447i \(0.593193\pi\)
\(744\) 4492.07 0.221354
\(745\) −20966.5 −1.03108
\(746\) −1564.25 −0.0767713
\(747\) −6887.73 −0.337361
\(748\) 17023.0 0.832116
\(749\) 9289.45 0.453176
\(750\) −4709.08 −0.229269
\(751\) −715.623 −0.0347716 −0.0173858 0.999849i \(-0.505534\pi\)
−0.0173858 + 0.999849i \(0.505534\pi\)
\(752\) 36266.4 1.75864
\(753\) −11148.4 −0.539536
\(754\) 41851.1 2.02139
\(755\) −24333.0 −1.17294
\(756\) −11047.9 −0.531491
\(757\) −32317.1 −1.55163 −0.775815 0.630960i \(-0.782661\pi\)
−0.775815 + 0.630960i \(0.782661\pi\)
\(758\) −16542.2 −0.792665
\(759\) −17978.4 −0.859783
\(760\) −13306.8 −0.635116
\(761\) −11740.3 −0.559247 −0.279623 0.960110i \(-0.590210\pi\)
−0.279623 + 0.960110i \(0.590210\pi\)
\(762\) 21723.6 1.03276
\(763\) −2036.43 −0.0966236
\(764\) −988.405 −0.0468053
\(765\) 18394.8 0.869364
\(766\) −11906.0 −0.561596
\(767\) −23387.0 −1.10098
\(768\) 15662.7 0.735911
\(769\) −18488.7 −0.866995 −0.433498 0.901155i \(-0.642721\pi\)
−0.433498 + 0.901155i \(0.642721\pi\)
\(770\) −51808.5 −2.42474
\(771\) 9075.59 0.423929
\(772\) 22582.9 1.05282
\(773\) −28213.0 −1.31274 −0.656372 0.754437i \(-0.727910\pi\)
−0.656372 + 0.754437i \(0.727910\pi\)
\(774\) 0 0
\(775\) −11198.9 −0.519068
\(776\) 8589.12 0.397334
\(777\) 2062.64 0.0952340
\(778\) −48537.7 −2.23671
\(779\) 1719.02 0.0790633
\(780\) −14529.7 −0.666982
\(781\) −26916.7 −1.23323
\(782\) −26750.3 −1.22326
\(783\) 22597.0 1.03136
\(784\) 1042.27 0.0474795
\(785\) −18487.7 −0.840578
\(786\) −10704.5 −0.485774
\(787\) −30281.3 −1.37155 −0.685776 0.727812i \(-0.740537\pi\)
−0.685776 + 0.727812i \(0.740537\pi\)
\(788\) −13043.1 −0.589644
\(789\) 348.454 0.0157228
\(790\) 2681.37 0.120758
\(791\) 25279.0 1.13631
\(792\) −12006.2 −0.538663
\(793\) −39134.3 −1.75246
\(794\) 22724.0 1.01567
\(795\) −30149.3 −1.34501
\(796\) 8938.63 0.398017
\(797\) 15491.1 0.688484 0.344242 0.938881i \(-0.388136\pi\)
0.344242 + 0.938881i \(0.388136\pi\)
\(798\) 14041.5 0.622887
\(799\) 31950.5 1.41468
\(800\) −17350.7 −0.766801
\(801\) 19305.5 0.851594
\(802\) 15872.4 0.698845
\(803\) 25168.9 1.10609
\(804\) 13307.7 0.583741
\(805\) 29098.8 1.27404
\(806\) 29631.0 1.29492
\(807\) −21257.5 −0.927259
\(808\) −12416.6 −0.540612
\(809\) −16916.7 −0.735179 −0.367590 0.929988i \(-0.619817\pi\)
−0.367590 + 0.929988i \(0.619817\pi\)
\(810\) 2978.26 0.129192
\(811\) −42803.7 −1.85332 −0.926659 0.375903i \(-0.877333\pi\)
−0.926659 + 0.375903i \(0.877333\pi\)
\(812\) −13362.9 −0.577521
\(813\) 1807.06 0.0779538
\(814\) −7116.56 −0.306432
\(815\) 26086.4 1.12118
\(816\) 17186.9 0.737331
\(817\) 0 0
\(818\) −2644.46 −0.113033
\(819\) 22953.9 0.979335
\(820\) 1589.04 0.0676729
\(821\) 14953.9 0.635683 0.317842 0.948144i \(-0.397042\pi\)
0.317842 + 0.948144i \(0.397042\pi\)
\(822\) 17975.9 0.762751
\(823\) −6802.39 −0.288112 −0.144056 0.989570i \(-0.546015\pi\)
−0.144056 + 0.989570i \(0.546015\pi\)
\(824\) 20957.9 0.886049
\(825\) −15950.3 −0.673114
\(826\) 20892.3 0.880069
\(827\) −43.8240 −0.00184270 −0.000921348 1.00000i \(-0.500293\pi\)
−0.000921348 1.00000i \(0.500293\pi\)
\(828\) −8452.48 −0.354763
\(829\) −16106.3 −0.674781 −0.337391 0.941365i \(-0.609544\pi\)
−0.337391 + 0.941365i \(0.609544\pi\)
\(830\) 20496.6 0.857166
\(831\) −15677.8 −0.654461
\(832\) 107.685 0.00448715
\(833\) 918.235 0.0381932
\(834\) 9373.10 0.389165
\(835\) 2673.74 0.110812
\(836\) −17315.8 −0.716365
\(837\) 15998.9 0.660697
\(838\) −35074.7 −1.44587
\(839\) 4269.60 0.175689 0.0878444 0.996134i \(-0.472002\pi\)
0.0878444 + 0.996134i \(0.472002\pi\)
\(840\) −10355.3 −0.425348
\(841\) 2943.17 0.120676
\(842\) 12795.5 0.523709
\(843\) −482.306 −0.0197052
\(844\) 3666.38 0.149529
\(845\) 43826.1 1.78422
\(846\) 28245.6 1.14788
\(847\) 29609.1 1.20116
\(848\) 52862.3 2.14068
\(849\) 10981.2 0.443903
\(850\) −23732.6 −0.957674
\(851\) 3997.10 0.161009
\(852\) 6743.57 0.271163
\(853\) 35651.3 1.43104 0.715521 0.698591i \(-0.246189\pi\)
0.715521 + 0.698591i \(0.246189\pi\)
\(854\) 34959.9 1.40082
\(855\) −18711.2 −0.748431
\(856\) −6406.18 −0.255793
\(857\) 11015.6 0.439072 0.219536 0.975604i \(-0.429546\pi\)
0.219536 + 0.975604i \(0.429546\pi\)
\(858\) 42202.6 1.67922
\(859\) 10268.1 0.407851 0.203925 0.978986i \(-0.434630\pi\)
0.203925 + 0.978986i \(0.434630\pi\)
\(860\) 0 0
\(861\) 1337.74 0.0529501
\(862\) 36158.7 1.42874
\(863\) −3943.51 −0.155549 −0.0777743 0.996971i \(-0.524781\pi\)
−0.0777743 + 0.996971i \(0.524781\pi\)
\(864\) 24787.4 0.976024
\(865\) −58894.9 −2.31501
\(866\) 1675.67 0.0657526
\(867\) 89.6795 0.00351289
\(868\) −9461.10 −0.369966
\(869\) −2783.70 −0.108666
\(870\) −26548.6 −1.03457
\(871\) −70032.4 −2.72440
\(872\) 1404.36 0.0545387
\(873\) 12077.5 0.468226
\(874\) 27210.4 1.05310
\(875\) −7912.72 −0.305713
\(876\) −6305.66 −0.243206
\(877\) 48677.1 1.87424 0.937120 0.349007i \(-0.113481\pi\)
0.937120 + 0.349007i \(0.113481\pi\)
\(878\) −19728.5 −0.758319
\(879\) −20860.4 −0.800459
\(880\) 64504.8 2.47097
\(881\) 4875.25 0.186437 0.0932186 0.995646i \(-0.470284\pi\)
0.0932186 + 0.995646i \(0.470284\pi\)
\(882\) 811.758 0.0309902
\(883\) −13952.6 −0.531759 −0.265880 0.964006i \(-0.585662\pi\)
−0.265880 + 0.964006i \(0.585662\pi\)
\(884\) 22443.9 0.853925
\(885\) 14835.7 0.563500
\(886\) 28854.4 1.09411
\(887\) −10494.9 −0.397275 −0.198638 0.980073i \(-0.563652\pi\)
−0.198638 + 0.980073i \(0.563652\pi\)
\(888\) −1422.44 −0.0537543
\(889\) 36502.4 1.37711
\(890\) −57449.6 −2.16372
\(891\) −3091.92 −0.116255
\(892\) −9515.56 −0.357180
\(893\) −32500.1 −1.21789
\(894\) −15257.2 −0.570781
\(895\) 47368.6 1.76911
\(896\) 26256.4 0.978979
\(897\) −23703.5 −0.882317
\(898\) 55877.2 2.07644
\(899\) 19351.5 0.717917
\(900\) −7498.98 −0.277740
\(901\) 46571.4 1.72200
\(902\) −4615.50 −0.170376
\(903\) 0 0
\(904\) −17432.9 −0.641382
\(905\) −793.169 −0.0291335
\(906\) −17707.0 −0.649311
\(907\) −1846.24 −0.0675892 −0.0337946 0.999429i \(-0.510759\pi\)
−0.0337946 + 0.999429i \(0.510759\pi\)
\(908\) 1994.15 0.0728836
\(909\) −17459.4 −0.637066
\(910\) −68306.6 −2.48829
\(911\) −26662.6 −0.969671 −0.484835 0.874605i \(-0.661121\pi\)
−0.484835 + 0.874605i \(0.661121\pi\)
\(912\) −17482.5 −0.634764
\(913\) −21278.8 −0.771332
\(914\) 38777.7 1.40334
\(915\) 24825.2 0.896934
\(916\) −25436.2 −0.917507
\(917\) −17987.0 −0.647745
\(918\) 33904.7 1.21898
\(919\) 26028.5 0.934279 0.467139 0.884184i \(-0.345285\pi\)
0.467139 + 0.884184i \(0.345285\pi\)
\(920\) −20067.1 −0.719123
\(921\) 22046.0 0.788753
\(922\) −23959.9 −0.855831
\(923\) −35488.2 −1.26556
\(924\) −13475.2 −0.479762
\(925\) 3546.20 0.126052
\(926\) 33126.2 1.17559
\(927\) 29469.7 1.04414
\(928\) 29981.6 1.06055
\(929\) 34867.3 1.23139 0.615693 0.787986i \(-0.288876\pi\)
0.615693 + 0.787986i \(0.288876\pi\)
\(930\) −18796.7 −0.662760
\(931\) −934.030 −0.0328803
\(932\) −26856.5 −0.943898
\(933\) −15552.6 −0.545732
\(934\) −50320.2 −1.76288
\(935\) 56828.4 1.98769
\(936\) −15829.5 −0.552780
\(937\) −13748.9 −0.479357 −0.239678 0.970852i \(-0.577042\pi\)
−0.239678 + 0.970852i \(0.577042\pi\)
\(938\) 62562.0 2.17774
\(939\) −15799.7 −0.549099
\(940\) −30042.7 −1.04243
\(941\) −42210.4 −1.46230 −0.731148 0.682219i \(-0.761015\pi\)
−0.731148 + 0.682219i \(0.761015\pi\)
\(942\) −13453.4 −0.465324
\(943\) 2592.35 0.0895211
\(944\) −26012.2 −0.896849
\(945\) −36881.4 −1.26958
\(946\) 0 0
\(947\) −12216.7 −0.419208 −0.209604 0.977786i \(-0.567217\pi\)
−0.209604 + 0.977786i \(0.567217\pi\)
\(948\) 697.413 0.0238934
\(949\) 33183.7 1.13508
\(950\) 24140.9 0.824456
\(951\) −21011.4 −0.716447
\(952\) 15995.8 0.544566
\(953\) 37883.5 1.28769 0.643845 0.765156i \(-0.277338\pi\)
0.643845 + 0.765156i \(0.277338\pi\)
\(954\) 41171.1 1.39724
\(955\) −3299.62 −0.111804
\(956\) 11848.7 0.400852
\(957\) 27561.7 0.930976
\(958\) −13616.7 −0.459223
\(959\) 30205.1 1.01707
\(960\) −68.3108 −0.00229659
\(961\) −16090.0 −0.540095
\(962\) −9382.79 −0.314463
\(963\) −9007.97 −0.301431
\(964\) −363.983 −0.0121609
\(965\) 75389.1 2.51488
\(966\) 21175.1 0.705277
\(967\) 9175.62 0.305138 0.152569 0.988293i \(-0.451245\pi\)
0.152569 + 0.988293i \(0.451245\pi\)
\(968\) −20419.0 −0.677987
\(969\) −15402.0 −0.510614
\(970\) −35940.4 −1.18967
\(971\) −27782.1 −0.918199 −0.459099 0.888385i \(-0.651828\pi\)
−0.459099 + 0.888385i \(0.651828\pi\)
\(972\) 17196.6 0.567471
\(973\) 15749.7 0.518924
\(974\) −24827.9 −0.816773
\(975\) −21029.6 −0.690756
\(976\) −43527.2 −1.42753
\(977\) 8808.24 0.288435 0.144217 0.989546i \(-0.453934\pi\)
0.144217 + 0.989546i \(0.453934\pi\)
\(978\) 18982.9 0.620662
\(979\) 59642.0 1.94706
\(980\) −863.407 −0.0281434
\(981\) 1974.73 0.0642693
\(982\) 53369.4 1.73430
\(983\) 45190.1 1.46627 0.733134 0.680085i \(-0.238057\pi\)
0.733134 + 0.680085i \(0.238057\pi\)
\(984\) −922.531 −0.0298874
\(985\) −43542.0 −1.40849
\(986\) 41009.4 1.32455
\(987\) −25291.5 −0.815642
\(988\) −22830.0 −0.735140
\(989\) 0 0
\(990\) 50238.7 1.61282
\(991\) 29048.5 0.931135 0.465567 0.885012i \(-0.345850\pi\)
0.465567 + 0.885012i \(0.345850\pi\)
\(992\) 21227.3 0.679401
\(993\) 23738.5 0.758630
\(994\) 31702.7 1.01162
\(995\) 29840.1 0.950748
\(996\) 5331.08 0.169600
\(997\) −20346.6 −0.646322 −0.323161 0.946344i \(-0.604745\pi\)
−0.323161 + 0.946344i \(0.604745\pi\)
\(998\) 19827.0 0.628870
\(999\) −5066.13 −0.160446
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1849.4.a.j.1.39 yes 50
43.42 odd 2 1849.4.a.i.1.12 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.12 50 43.42 odd 2
1849.4.a.j.1.39 yes 50 1.1 even 1 trivial